Mourinho was booked by referee Mike Dean in the 77th minute after the Portuguese approached the Southampton bench.
United's victory was the first loss for Son and Spurs since Jose Mourinho replaced Mauricio Pochettino, who was sacked a fortnight ago due to Spurs lacklustre campaign so far.
His remarks came after Tottenham's 1-2 defeat against United on Wednesday (local time).
Tottenham will next take on Burnley while United will face Manchester City on Saturday, December 7.
Addressing media in his first press conference after inking a deal with the North London club, the former Chelsea gaffer said the pool of talent in hand is the biggest gift Tottenham have.
Harry Redknapp said the rivalry is no reason for Pochettino to reject a move to the Emirates as fans would love any manager who can win games for their side - even if it is Saddam Hussein.
The former Chelsea and Manchester United manager has signed a contract that runs until the end of the 2022/23 season, the north London club said in an online statement.
Pochettino had transformed Spurs' fortunes since arriving from Southampton in 2014 despite failing to win a trophy in his five-and-a-half years in charge.
The 32-year-old made an error while trying to collect a simple cross into the box and fell inside the net in an odd angle.
In Madrid, record 13-time champions Real were 2-0 down at half-time against Club Brugge, for whom Nigerian forward Emmanuel Dennis scored a first-half brace.
The unique 29th-minute goal gave Spurs the lead but they lost 1-2 eventually with Ricardo Pereira (69th minute ) and James Maddison (85th) minute scoring for Leicester.
By the time Otamendi finished off Aguero's cross in the 18th minute, City had established the fastest 5-0 lead in the Premier League era.
David Beckham has told Mauricio Pochettino he wishes he could play for Tottenham Hotspur at the club's new stadium after watching their 4-0 home win over Crystal Palace.
Harry Kane stepped up his bid to win the Premier League's golden boot as Tottenham warmed up for the FA Cup semi-finals with a 1-1 draw at Brighton.
Combined with Chelsea’s defeat at Manchester United, the win moved his side back into the top four despite a less than convincing performance.